Exposure method, exposure apparatus, and method of manufacturing device

ABSTRACT

An exposure method comprises a calculation step of calculating a correction amount of a correction unit which corrects a change in imaging characteristics of a projection optical system based on at least one of parameters including a numerical aperture and effective light source of an illumination optical system, a numerical aperture of the projection optical system, and a size and pitch of a pattern, and an amount of change in environment condition in the projection optical system; and a correction step of making the correction unit operate in accordance with the correction amount calculated in the calculation step.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an exposure method, an exposureapparatus, and a method of manufacturing a device by using the exposureapparatus.

2. Description of the Related Art

In a projection exposure apparatus, when environment conditions such asatmospheric pressure, temperature, and humidity vary, the imagingcharacteristics of a projection optical system change. With recentminiaturization of semiconductor devices, demands have arisen forincreases in the accuracy of imaging characteristics influenced byvariations in environment conditions. This makes it necessary to correctthe imaging characteristics. For example, Japanese Patent Laid-Open No.7-183210 discloses a method of correcting changes in imagingcharacteristics due to variations in environment conditions. JapanesePatent Laid-Open No. 7-183210 discloses a method of detecting a changein atmospheric pressure as one of environment conditions and correctingchanges in projection magnification and focus position with the changein atmospheric pressure by driving an optical member in a projectionoptical system in the optical axis direction. Letting ΔP be anatmospheric pressure change and K be an atmospheric pressure correctioncoefficient for a projection magnification, a projection magnificationchange ΔM_(P) due to an atmospheric pressure change can be expressed byΔM _(P) =K _(M) ×ΔP   (1)where K_(M) is the coefficient determined by the characteristics of theprojection optical system. This technique corrects imagingcharacteristics by calculating the driving amount of the projectionoptical system in the optical axis direction from ΔM_(P) calculated byusing equation (1).

The amount of change in aberration per unit atmospheric pressure isconstant. However, the diffracted light intensity distribution withinthe pupil plane varies depending on the effective light source of anillumination optical system (the light intensity distribution in thepupil plane), the numerical aperture of a projection optical system, amask, and conditions for the pattern of the mask. For this reason,changes in imaging characteristics due to changes in atmosphericpressure differ for the respective conditions described above. The sameapplies to changes in imaging characteristics accompanying the abovechanges in atmospheric pressure. If, therefore, the correctioncoefficient K_(M) described above is uniquely determined regardless ofthe effective light source of the illumination optical system, thenumerical aperture of the projection optical system, and the pattern ofa mask, it is impossible to accurately correct changes in imagingcharacteristics due to changes in atmospheric pressure.

SUMMARY OF THE INVENTION

The present invention accurately corrects changes in the imagingcharacteristics of a projection optical system due to changes inenvironment conditions within the projection optical system.

According to the present invention, there is provided an exposure methodof illuminating a mask, on which a pattern is formed, by using anillumination optical system, and projecting the illuminated pattern ontoa substrate through a projection optical system, the method comprising acalculation step of calculating a correction amount of a correction unitwhich corrects a change in imaging characteristics of the projectionoptical system based on at least one of parameters including a numericalaperture and effective light source of the illumination optical system,a numerical aperture of the projection optical system, and a size andpitch of the pattern, and an amount of change in environment conditionin the projection optical system; and a correction step of making thecorrection unit operate in accordance with the correction amountcalculated in the calculation step.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view showing the arrangement of a projection exposureapparatus according to the first and second embodiments;

FIG. 2 is a flowchart for an exposure method according to the firstembodiment; and

FIG. 3 is a flowchart for an exposure method according to the secondembodiment.

DESCRIPTION OF THE EMBODIMENTS

The embodiments of an exposure method and exposure apparatus accordingto the present invention will be described in detail below withreference to the accompanying drawings.

[First Embodiment]

FIG. 1 is a view showing the arrangement of an exposure apparatusaccording to an embodiment of the present invention. The firstembodiment shows an example of correcting changes in the imagingcharacteristics of a projection optical system due to changes inatmospheric pressure as one of environment conditions within theprojection optical system (a housing accommodating an optical system).Environment conditions which change within the projection optical systemcan be at least an atmospheric pressure, temperature, or humidity. Theimaging characteristics of the projection optical system which arecorrection targets in the first embodiment include a projectionmagnification and a best focus position. However, imagingcharacteristics such as distortion aberration and curvature of field canbe correction targets. Exposure light emitted from a light source 1passes through an illumination optical system 2, and illuminates a mask(reticle) 3 on which a pattern is formed. A reticle stage 4 holds thereticle 3. The pattern of the reticle 3 is transferred onto a wafer(substrate) 6 through a projection optical system 5. An optical element5 a of the optical elements included in the projection optical system 5is configured to move in a direction (Z direction) parallel to theoptical axis of the projection optical system 5. An optical systemcontroller 8 controls the movement of the optical element 5 a. Referencenumeral 5 b denotes a measurement device (barometer) which is placed inthe projection optical system 5 and measures the amount of change inpressure. A wafer stage (substrate stage) 7 is configured to hold thewafer 6 and move in the X, Y, and Z directions. A wafer stage controller9 controls the movement of the wafer stage 7.

A storage unit 10 stores a table of sensitivities to atmosphericpressure and a table of sensitivities to driving (both of which will bedescribed later). An input unit 11 receives, as an exposure recipe, atleast one parameter of the numerical aperture and effective light sourceof the illumination optical system 2, the numerical aperture of theprojection optical system 5, and the size and pitch of a pattern. Thestorage unit 10 then stores the exposure recipe. A main controller 12reads out parameters such as a numerical aperture and the table ofsensitivities to atmospheric pressure from the storage unit 10, andcalculates the amounts of change in imaging characteristics based on thereadout information and the amount of change in atmospheric pressuremeasured by a barometer 5 b. The main controller 12 reads out the tableof sensitivities to driving from the storage unit 10, and calculates thedriving amounts (the correction amounts of the correction units) of thewafer stage 7 and optical element 5 a based on the readout information,the parameters, and the calculated amounts of change in imagingcharacteristics. The main controller 12 issues commands to the opticalsystem controller 8 and the wafer stage controller 9 to make the waferstage 7 and the optical element 5 a operate in accordance with thecalculated driving amounts. In the first embodiment, the optical systemcontroller 8 and the wafer stage controller 9 form correction unitswhich correct a change in the imaging characteristics of the projectionoptical system due to a change in environment condition in theprojection optical system by moving the wafer stage 7 and the opticalelement 5 a in the Z direction. The main controller 12 serves as acontroller which calculates the correction amounts of the correctionunits (the optical system controller 8 and the wafer stage controller 9)which correct a change in the imaging characteristics of the projectionoptical system 5.

FIG. 2 is a flowchart showing a method of exposing a pattern on thewafer 6 upon correcting a change in the imaging characteristics of theprojection optical system 5 due to a change in atmospheric pressure byusing the exposure apparatus in FIG. 1. In step S101, the designatedreticle 3 is loaded onto the reticle stage 4. In step S102, the inputunit 11 receives the effective light source of the illumination opticalsystem 2, the numerical aperture of the projection optical system 5, andcorrespondence tables of sensitivities to atmospheric pressure andsensitivities to driving, which are suitable for the transfer of thepattern formed on the loaded reticle 3 onto the wafer 6. In this case,the storage unit 10 stores the correspondence tables of sensitivities toatmospheric pressure and sensitivities to driving. Step S102 forms theobtaining step of obtaining an effective light source, the numericalaperture of the projection optical system 5, and tables of sensitivitiesto atmospheric pressure and sensitivities of driving. In step S103, thewafer 6 is loaded on the wafer stage 7. In step S104, the wafer stagecontroller 9 drives the wafer stage 7 in the plane direction of thewafer so as to transfer the pattern at a desired position on the wafer.

In step S105, the main controller 12 calculates the amounts of change inimaging characteristics due to a change in atmospheric pressure. StepS105 forms the first calculation step of calculating the amounts ofchange in imaging characteristics. The first embodiment has exemplifiedthe best focus position and the projection magnification as imagingcharacteristics as correction targets. However, it is possible to setother imaging characteristics (distortion aberration and curvature offield) as correction targets. An atmospheric pressure change ΔP which isthe difference between an atmospheric pressure measurement value P_(M)of the barometer 5 b and a reference atmospheric pressure (e.g., 1013hPa) P_(R) can be given byΔP=P _(M) −P _(R)   (2)In addition, the relationships between changes in atmospheric pressureand the amounts of change in imaging characteristics can be given byΔF _(P) =K _(F) ×ΔP   (3)ΔM _(P) =K _(M) ×ΔP   (4)where ΔF_(P) and ΔM_(P) are the best focus position of the projectionoptical system 5 and the amount of change in projection magnification,respectively, and K_(F) and K_(M) are a best focus position per unitatmospheric pressure and the amount of change in projectionmagnification (to be expressed as sensitivities to atmospheric pressurehereinafter), respectively. The sensitivities K_(F) and K_(M) toatmospheric pressure are the first correction coefficients which definethe relationship between the amount of change in environment condition(pressure) and the amounts of change in imaging characteristics (thebest focus position and the projection magnification) due to the changein environment condition. The sensitivities K_(F) and K_(M) toatmospheric pressure are also coefficients determined by at least one ofthe above parameters including the effective light source of theillumination optical system, the numerical aperture of the projectionoptical system 5, and the pattern of the reticle 3. For this reason, acorrespondence table of the sensitivities K_(F) and K_(M) to atmosphericpressure and at least one parameter is obtained in advance by opticalcalculation or experiment. This table is input in step S102 and storedin the storage unit 10. The main controller 12 then obtains thenecessary sensitivities K_(F) and K_(M) to atmospheric pressure byreferring to the correspondence table of the sensitivities K_(F) andK_(M) to atmospheric pressure.

In step S106, the main controller 12 determines whether to correctchanges in imaging characteristics due to a change in atmosphericpressure. Step S106 is the determination step of determining whether toexecute the second calculation step and the correction step (to bedescribed later), depending on whether the calculated amounts of changein imaging characteristics fall within allowable ranges. If the amountsof change in the best focus position of the projection optical systemand projection magnification due to the change in atmospheric pressurefall within the allowable ranges, the process advances to step S109 toperform exposure. If the change amounts ΔF_(P) and ΔM_(P) fall outsidethe allowable ranges, the main controller 12 advances to step S107 tocalculate the correction amounts of the correction units which correctthe changes in imaging characteristics. In step S107, the maincontroller 12 calculates the driving amounts (correction amounts) of thewafer stage 7 and optical element 5 a in the projection optical system5. Step S107 forms the second calculation step of calculating thecorrection amounts of the correction units. Steps S105 and S107 form thecalculation step of calculating the correction amounts of the correctionunits based on at least one parameter and the amounts of change inenvironment conditions in the projection optical system. This embodimenthas exemplified the case in which imaging characteristics are correctedby driving the wafer stage 7 and the optical element 5 a. However, thepresent invention is not limited to any specific correction technique aslong as imaging characteristics as correction targets can be corrected.Letting ΔT_(X) be the driving amount of the wafer stage 7 in the opticalaxis direction and ΔT_(Y) be the driving amount of the optical element 5a in the optical axis direction, the relationship between the amounts ofchanges ΔF_(P) and ΔM_(P) of imaging characteristics can be representedby equation (5) given below. This makes it possible to calculate thedriving amounts ΔT_(X) and ΔT_(Y).

$\begin{matrix}{\begin{bmatrix}{\Delta\; F_{P}} \\{\Delta\; M_{P}}\end{bmatrix} = {\begin{bmatrix}X_{F} & Y_{F} \\X_{M} & Y_{M}\end{bmatrix}\begin{bmatrix}{\Delta\; T_{X}} \\{\Delta\; T_{Y}}\end{bmatrix}}} & (5)\end{matrix}$where X_(F) and X_(M) are respectively the amounts of change in bestfocus position and projection magnification per unit driving amount ofthe wafer stage 7 (to be expressed as sensitivities to driving of thewafer stage hereinafter) in the optical axis direction, and Y_(F) andY_(M) are respectively the amounts of change in best focus position andprojection magnification per unit driving amount of the optical element5 a (to be expressed as sensitivities to driving of the optical elementhereinafter) in the optical axis direction. The sensitivities X_(F) andX_(M) to driving of the wafer state and the sensitivities Y_(F) andY_(M) to driving of the optical element are the second correctioncoefficients which define the relationship between the amounts of changein the imaging characteristics of the projection optical system 5 andthe correction amounts of the correction units. The sensitivities X_(F),X_(M), Y_(F), and Y_(M) to driving are coefficients determined by atleast one of the above parameters including the effective light sourceof the illumination optical system, the numerical aperture of theprojection optical system 5, and the pattern of the reticle 3. For thisreason, a correspondence table of the sensitivities X_(F), X_(M), Y_(F),and Y_(M) to driving and at least one parameter is obtained in advanceby optical calculation or experiment. This table is input in step S102and stored in the storage unit 10.

In step S108, the wafer stage controller 9 and the optical systemcontroller 8 adjust imaging characteristics by driving the wafer stage 7and the optical element 5 a in the optical axis direction. Step S108forms the correction step of making the correction units operate inaccordance with calculated correction amounts. The main controller 12issues a command to the wafer stage controller 9 to drive the waferstage 7 to a position TP_(X) in the optical axis direction. The waferstate position TP_(X) can be expressed by equation (6) given below. Themain controller 12 also issues a command to the optical systemcontroller 8 to drive the optical element 5 a to a position TP_(Y) inthe optical axis direction. The optical element position TP_(Y) can begiven by equation (7) given below.TP _(X) =TP _(XR) +ΔT _(X)   (6)TP _(Y) =TP _(YR) +ΔT _(Y)   (7)where TP_(XR) is the position of the wafer stage 7 in the optical axisdirection at the reference atmospheric pressure P_(R), and TP_(YR) isthe position of the optical element 5 a in the optical axis direction atthe reference atmospheric pressure P_(R). It is possible to correctchanges in best focus position and projection magnification due to achange in atmospheric pressure, as described above.

In step S109, exposure light from the light source 1 illuminates thereticle 3. The pattern on the reticle 3 is transferred onto an exposuretarget area on the wafer 6 through the projection optical system 5. Instep S110, the main controller 12 determines whether pattern transfer toall the exposure target shots within the wafer is complete. If thepattern transfer is complete, the process advances to step S111. If thepattern transfer is not complete, the process returns to step S104 torepeat steps S104 to S109 until the pattern transfer is complete. Instep S111, the wafer 6 having undergone exposure is unloaded. In stepS112, the main controller 12 determines whether pattern transfer to allthe wafers of the lot is complete. If the pattern transfer is complete,exposure is complete. If the pattern transfer is not complete, the maincontroller 12 repeats steps S103 to S111.

As described above, according to this embodiment, it is possible tocorrect a change in imaging characteristics due to a change inenvironment condition in the projection optical system for each of thefollowings: the effective light source of the illumination opticalsystem, the numerical aperture of the projection optical system, and areticle condition. Note that the above embodiment has presented the twoimaging characteristics as correction targets, namely the best focusposition and the projection magnification. However, the types and numberof imaging characteristics as correction targets are not specificallylimited. However, the number of correction units needs to be equal to ormore than the number of imaging characteristics as correction targets.

[Second Embodiment]

Another embodiment of the present invention will be described withreference to FIGS. 1 and 3. The first embodiment obtains the necessaryvalues of sensitivity to atmospheric pressure and sensitivity to drivingby referring to the correspondence table of sensitivities to atmosphericpressure, sensitivities to driving, and at least one parameter. In thesecond embodiment, however, sensitivity to atmospheric pressure andsensitivity to driving are expressed as function expressions forparameters instead of a correspondence table of parameters. Substitutingparameters into the function expressions yields the necessary values ofsensitivity to atmospheric pressure and sensitivity to driving.

Since steps S201, S203, and S204 are the same as steps S101, S103, andS104 in the first embodiment. In step S202, parameters such as theeffective light source of an illumination optical system 2 and thenumerical aperture of a projection optical system 5 which are suitablefor the transfer of the pattern formed on a loaded reticle 3 onto awafer 6 are input. In step S102 corresponding to the first embodiment,sensitivities to atmospheric pressure and sensitivities to driving areinput in addition to the effective light source of the illuminationoptical system 2 and the numerical aperture of the projection opticalsystem 5. In step S202, function expressions for sensitivities toatmospheric pressure and sensitivities to driving are input.

In step S205, a main controller 12 calculates the amounts of change inimaging characteristics due to a change in atmospheric pressure. In thefirst embodiment, with regard to the sensitivities K_(F) and K_(M) toatmospheric pressure, the main controller 12 calculates the amounts ofchanges ΔF_(P) and ΔM_(P) in imaging characteristics by using numericalvalues in the correspondence table obtained in advance. In the secondembodiment, in step S105, the main controller 12 calculates parametersK_(F) and K_(M) dependent on the effective light source of theillumination optical system, the numerical aperture of the projectionoptical system 5, and the size and pitch of the pattern of the reticle3. The sensitivities K_(F)

and K_(M) to atmospheric pressure are expressed by function equations(11) and (12) using the numerical apertures of the projection opticalsystem 5 and illumination optical system 2 as parameters.K _(F) =A _(F) ×NA _(ul){circumflex over (])}2+B _(r) ×NA _(il)^2+C _(F)×NA _(ul) ×NA _(il) +D _(F) ×NA _(ul) +E _(F) ×NA _(il) +F _(F)   (11)K _(M) =A _(M) ×NA _(ul)^2+B _(M) ×NA _(il)^2+C _(M) ×NA _(ul) ×NA _(il)+D _(M) ×NA _(ul) +E _(M) ×NA _(il) +F _(M)   (12)where NA_(ul) is the numerical aperture of the projection optical system5, and NA_(il) is the numerical aperture of the illumination opticalsystem 2. Function equations (11) and (12) express the sensitivitiesK_(F) and K_(M) to atmospheric pressure by using the numerical apertureof the projection optical system 5 and the numerical aperture of theillumination optical system 2 as parameters. Parameters expressing thesensitivities K_(F) and K_(M) to atmospheric pressure are not limited aslong as they are a parameter for a reticle loaded in step S201 and aparameter input in step S202. In addition, equations (11) and (12) areexpressed by quadratic functions. However, the degrees and functionsthat express function expressions are not specifically limited. It ispossible to obtain coefficients A_(F) to F_(F) and A_(M) to F_(M) offunction equations (11) and (12) in advance by optical calculation orexperiment and store them in a storage unit 10 in advance. It ispossible to calculate the amounts of change ΔF_(P) and ΔM_(P) by usingthe coefficients A_(F) to F_(F) and A_(M) to F_(M) stored in the storageunit 10, the reticle 3 loaded in step S201, the effective light sourceof the illumination optical system input in step S202, and the numericalaperture of the projection optical system 5. Step S206 is the same asstep S106 in the first embodiment.

In step S207, the main controller 12 calculates the driving amounts of awafer stage 7 and an optical element 5 a in the projection opticalsystem 5. This embodiment corrects imaging characteristics by drivingthe wafer stage 7 and the optical element 5 a. However, the correctiontechnique to be used is not specifically limited as long as imagingcharacteristics as correction targets can be corrected. Letting ΔT_(X)be the driving amount of the wafer stage 7 in the optical axis directionand ΔT_(Y) be the driving amount of the optical element 5 a in theoptical axis direction, the relationship between the amounts of changeΔF_(P) and ΔM_(P) of imaging characteristics can be represented byequation (13) given below. This makes it possible to calculate thedriving amounts ΔT_(X) and ΔT_(Y).

$\begin{matrix}{\begin{bmatrix}{\Delta\; F_{P}} \\{\Delta\; M_{P}}\end{bmatrix} = {\begin{bmatrix}X_{F} & Y_{F} \\X_{M} & Y_{M}\end{bmatrix}\begin{bmatrix}{\Delta\; T_{X}} \\{\Delta\; T_{Y}}\end{bmatrix}}} & (13)\end{matrix}$where X_(F) and X_(M) are respectively the amounts of change in bestfocus position and projection magnification per unit driving amount ofthe wafer stage 7 (to be expressed as sensitivities to driving of thewafer stage hereinafter) in the optical axis direction, and Y_(F) andY_(M) are respectively the amounts of change in best focus position andprojection magnification per unit driving amount of the optical element5 a (to be expressed as sensitivities to driving of the optical elementhereinafter) in the optical axis direction. The sensitivities X_(F) andX_(M) to driving of the wafer state and the sensitivities Y_(F) andY_(M) to driving of the optical element are parameters dependent on theeffective light source of the illumination optical system 2 input instep S202, the numerical aperture of the projection optical system 5,and the size and pitch of the pattern of the reticle 3. Thesensitivities X_(F) and X_(M) to driving of the wafer stage and thesensitivities Y_(F) and Y_(M) to driving of the optical element areexpressed by function equations (14) to (17) given below using thenumerical aperture of the projection optical system 5 and the numericalaperture of the illumination optical system 2 as parameters.X _(P) =A _(FX) ×NA _(ul)^2+B _(FX) ×NA _(ul)^2+C _(FX) ×NA _(ul) ×NA_(il) +D _(FX) ×NA _(ul) +E _(FX) ×NA _(il) +F _(FX)   (14)X _(M) =A _(MX) ×NA _(ul)^2+B _(MX) ×NA _(ul)^2+C _(MX) ×NA _(ul) ×NA_(il) +D _(MX) ×NA _(ul) +E _(MX) ×NA _(il) +F _(MX)   (15)Y _(F) =A _(FY) ×NA _(ul)^2+B _(FY) ×NA _(il)^2+C _(FY) ×NA _(ul) ×NA_(il) +D _(FY) ×NA _(ul) +E _(FY) ×NA _(il) +F _(FY)   (16)Y _(M) =A _(MY) ×NA _(ul)^2+B _(MY) ×NA _(il)^2+C _(MY) ×NA _(ul) ×NA_(il) +D _(MY) ×NA _(ul) +E _(MY) ×NA _(il) +F _(MY)   (17)where NA_(ul) is the numerical aperture of the projection optical system5, and NA_(il) is the numerical aperture of the illumination opticalsystem 2. Equations (14) to (17) express the sensitivities X_(F) andX_(M) to driving of the wafer stage and the sensitivities Y_(F) andY_(M) to driving of the optical element by using the numerical apertureof the projection optical system 5 and the numerical aperture of theillumination optical system 2 as parameters. Parameters expressing thesensitivities X_(F) and X_(M) to driving of the wafer stage and thesensitivities Y_(F) and Y_(M) to driving of the optical element are notlimited as long as they are parameters for a reticle loaded in step S201and parameters input in step S202. In addition, equations (14) to (17)are expressed by quadratic functions. However, the degrees and functionswhich express function expressions are not specifically limited. It ispossible to obtain coefficients A_(FX) to F_(FX), A_(MX) to F_(MX),A_(FY) to A_(FY), and A_(MY) to F_(MY) of equations (14) to (17) inadvance by optical calculation or experiment and store them in thestorage unit 10 in advance. It is possible to calculate the drivingamounts ΔT_(X) and ΔT_(Y) by using the coefficients A_(FX) to F_(FX),A_(MX) to F_(MX), A_(FY) to F_(FY), and A_(MY) to F_(MY), the reticle 3loaded in step S201, the effective light source of the illuminationoptical system input in step S202, and the numerical aperture of theprojection optical system 5.

Steps S208 to S212 are the same as steps S108 to S112 in the firstembodiment.

A method of manufacturing a device using the above exposure apparatuswill be described next. Devices are manufactured by a step oftransferring by exposure a pattern onto a substrate 6 using the exposureapparatus described above, a step of developing the substrate 6 exposedin the exposing step, and other known steps of processing the substrate6 developed in the developing step. For example, the devices can be asemiconductor integrated circuit device, liquid crystal display device,and the like. The substrate 6 can be a wafer, glass plate, or the like.The known steps are, for example, oxidation, film formation, deposition,doping, planarization, dicing, bonding, and packaging steps.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2009-158196, filed Jul. 2, 2009, which is hereby incorporated byreference herein in its entirety.

What is claimed is:
 1. An exposure method of illuminating a mask, onwhich a pattern is formed, using an illumination optical system, andprojecting an image of a pattern of the illuminated mask onto asubstrate through a projection optical system, the method comprising: anobtaining step of obtaining data of an amount of change in anenvironment condition in the projection optical system and data of atleast one of parameters, including a numerical aperture and effectivelight source of the illumination optical system, a numerical aperture ofthe projection optical system, and a size and pitch of the pattern; acalculation step of calculating a correction amount of a correction unitwhich corrects a change in imaging characteristics of the projectionoptical system based on a first coefficient defining a relationshipbetween the amount of change in the environment condition and an amountof change in imaging characteristics of the projection optical systemand a second coefficient defining a relationship between the amount ofchange in imaging characteristics of the projection optical system andthe correction amount of the correction unit; and a correction step ofmaking the correction unit operate in accordance with the correctionamount calculated in the calculation step, wherein values of the firstcoefficient and the second coefficient are determined by a value of atleast one of the parameters, wherein the calculation step includes: afirst calculation step of calculating an amount of change in imagingcharacteristics of the projection optical system using the amount ofchange in the environment condition and the first coefficient, and asecond calculation step of calculating a correction amount of thecorrection unit using the amount of change in the imagingcharacteristics calculated in the first calculation step, and the secondcoefficient.
 2. The method according to claim 1, wherein: in the firstcalculation step, data of the first coefficient is obtained by referringto a correspondence table of the first coefficient and the at least oneof the parameters, and in the second calculation step, data of thesecond coefficient is obtained by referring to a correspondence table ofthe second coefficient and the at least one of the parameters.
 3. Themethod according to claim 1, wherein: the first coefficient and thesecond coefficient are respectively expressed by function expressionsbased on the at least one of the parameters, in the first calculationstep, a value of the first coefficient is calculated by substituting thevalue of the at least one of the parameters into a function expressionexpressing the first coefficient using the at least one of theparameters, and in the second calculation step, a value of the secondcoefficient is calculated by substituting a value of the at least one ofthe parameters into a function expression expressing the secondcoefficient using the at least one of the parameters.
 4. The methodaccording to claim 1, wherein: the environment condition is at least oneof an atmospheric pressure, a temperature, or a humidity in theprojection optical system, the imaging characteristic is at least one ofa projection magnification, distortion aberration, curvature of field,or a best focus position, and the correction amount of correction unitis a movement amount of at least one of a substrate stage which holdsthe substrate or an optical element included in the projection opticalsystem.
 5. The method according to claim 1, further comprising adetermination step of determining whether to execute the secondcalculation step and the correction step, depending on whether theamount of change in imaging characteristics calculated in the firstcalculation step falls within an allowable range.
 6. An exposureapparatus which illuminates a mask, on which a pattern is formed, byusing an illumination optical system, and projects an image of a patternof the illuminated mask onto a substrate through a projection opticalsystem, the apparatus comprising: an obtaining unit which obtains dataan amount of change in an environment condition in the projectionoptical system and data of at least one of parameters, including anumerical aperture and effective light source of the illuminationoptical system, a numerical aperture of the projection optical system,and a size and pitch of the pattern; a correction unit which corrects achange in imaging characteristics of the projection optical system; anda controller which controls said correction unit, wherein saidcontroller is configured to: calculate a correction amount of saidcorrection unit which corrects the change in imaging characteristics ofthe projection optical system, based on a first coefficient defining arelationship between the amount of change in the environment conditionand an amount of change in imaging characteristics of the projectionoptical system and a second coefficient defining a relationship betweenthe amount of change in imaging characteristics of the projectionoptical system and the correction amount of the correction unit; andcause said correction unit to operate in accordance with the calculatedcorrection amount, wherein values of the first coefficient and thesecond coefficient are determined by a value of at least one of theparameters, and wherein said controller is configured to: calculate anamount of change in imaging characteristics of the projection opticalsystem using the amount of change in the environment condition and thefirst coefficient; and calculate a correction amount of the correctionunit using the calculated amount of change in imaging characteristicsand the second coefficient.
 7. A method of manufacturing a device, themethod comprising: exposing a substrate using an exposure apparatus;developing the exposed substrate; and processing the developed substrateto manufacture the device, said exposure apparatus comprising: anillumination optical system which illuminates a mask on which a patternis formed; a projection optical system which projects an image of apattern of the illuminated mask onto a substrate; an obtaining unitwhich obtains data of an amount of change in an environment condition inthe projection optical system and data of at least one of parameters,including a numerical aperture and effective light source of theillumination optical system, a numerical aperture of the projectionoptical system, and a size and pitch of the pattern; a correction unitwhich corrects a change in imaging characteristics of said projectionoptical system; and a controller which controls said correction unit,wherein said controller is configured to: calculate a correction amountof said correction unit which corrects the change in imagingcharacteristics of said projection optical system, based on a firstcoefficient defining a relationship between the amount of change in theenvironment condition and an amount of change in imaging characteristicsof the projection optical system and a second coefficient defining arelationship between the amount of change in imaging characteristics ofthe projection optical system and the correction amount of thecorrection unit; and cause said correction unit to operate in accordancewith the calculated correction amount, wherein values of the firstcoefficient and the second coefficient are determined by a value of atleast one of the parameters, and wherein said controller is configuredto: calculate an amount of change in imaging characteristics of theprojection optical system using the amount of change in the environmentcondition and the first coefficient; and calculate a correction amountof the correction unit using the calculated amount of change in imagingcharacteristics and the second coefficient.